(A) : If the perimeter of a rectangle is 12 meters, then its maximum area is 9 $$m^2$$.
(R) : Geometric mean of two positive numbers is less than or equal to their Arithmetic mean

Geometric mean of numbers a and b is 

$$=√ab.$$ and Arithmetic mean

$$=(a+b)/2$$.

we know that ,Geometric mean of two positive numbers is less than or equal to their Arithmetic mean.

So, Condition R is correct.

Condition A:

Let say ,length and breadth of the rectangle are l & b respectively.

So, $$2(l+b)=12.$$

Or,$$(l+b)=6.$$

And Area $$=lb$$.

multiplication of two numbers achieve when they are both equal in equation 1.

So,$$l=b=3.$$

Then only it can attain maximum value of 

$$3×3=9$$m^2.

So, condition 'A' is true and correct explanation made by 'R'.

So,Option A is correct choice.